VARIABLES AFFECTING TUBING PRESSURE LOSS The variables that affect vertical pressure losses in tubing are tubing size, flow rate, density and density and viscosity . Because there is probably more than one phase flowing, we must add two more variables: gas-liquid ratio and water-oil ratio. ratio . Finally we should add the effect of slippage of slippage..
TUBING SIZE
Suppose that we increase the tubing size in a well from inches to 3 inches, leaving all other parameters constant. The result, as shown in Figure 1 , is that the total pressure loss that occurs between the formation and the surface drops from 1900 psi for the smaller tubing string to 900 psi for the larger string.
This substantial pressure drop reflects the reduction in friction pressure for the larger-diameter tubing. We conclude, then, that under these conditions, as the tubing size increases, the pressure losses will decrease.
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FLUID DENSITY The second variable to consider is fluid density, which, for oil, we may express in terms of API gravity. For the well of Figure of Figure 2 we see that the pressure loss over an 8000 foot interval is approximately 1700 psi if it is flowing brine, but only 1200 psi if it is flowing a 50-degree API oil.
We conclude that for similar flowing conditions, pressure losses will be lower for lower fluid densities. At higher fluid densities, the hydrostatic pressure gradient becomes the dominant component of pressure loss.
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FLUID VISCOSITY In Figure 3 we see that higher viscosities give higher pressure losses, again due to an increase in friction pressure.
At a fluid viscosity of 50 cp, the total pressure loss over the 8000-ft interval is 1900 psi; at 1 cp, the total pressure loss is 1200 psi. Note that the effect is much less pronounced as the viscosity decreases from 10 cp to 1 cp. We conclude, then, that the viscosity of the flowing fluid is an important variable and that lower-viscosity oils under similar conditions will have lower friction pressure losses.
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GAS-LIQUID RATIO In Figure 4 , we see that at a GLR of 250 SCF/STB, the pressure loss from the formation to the surface is about 1900 psi, whereas at a GLR of 5000 SCF/STB, the pressure loss is about 700 psi.
In both cases the surface pressure is assumed to be 100 psi. Thus, at a GLR of 250 SCF/STB, this well will flow if the bottomhole pressure exceeds (1900+100), or 2000 psi, while at a GLR of 5000 SCF/STB, the well will flow if the bottomhole pressure exceeds (700+100), or 800 psi. In general, then, the higher the GLR at a given flow rate, the lower will be the tubing pressure loss—but loss— but only up to a point . While higher GLRs reduce a fluid's density, resulting in lower hydrostatic pressure, they also result in higher friction pressure losses, which offset this hydrostatic pressure decrease. The decrease in the hydrostatic pressure is overcome by the increase in the friction losses. At some limiting value of GLR, the increase in friction pressure becomes approximately equal to the decrease in hydrostatic pressure, and above this limt, the total pressure loss actually begins to increase.
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WATER-OIL RATIO We see in Figure 5 that as the water-oil ratio (WOR) increases from 0 to 1000, the pressure losses in the tubing also increase.
This means that it will require a higher bottomhole flowing pressure to lift produced liquids that have water in them. The greater the WOR, the greater the pressure needed because water is slightly denser than oil. The magnitude of the pressure increase is not as large as those noted with other variables.
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SLIPPAGE AND HOLDUP In order to illustrate the condition of holdup, which results from slippage, we plot the bottomhole flowing pressure at different flow rates for several GLR’s. In Figure 6 we see that for a GLR of 800 the bottomhole flowing pressure required to maintain flow increases as the flow rate increases.
This is as we might expect. At the higher flow rates the frictional losses increase and so will the required bottomhole flowing pressure. At lower flow rates the frictional losses are smaller and so the bottomhole flowing pressure required to maintain flow is lower. At lower GLR’s, however, we see that the curves have a point of reversal or minimum. For the 400 GLR curve we see that the required bottomhole pressure decreases as we reduce the rate until at about 150 BOPD it begins to increase again. This reversal, or holdup, holdup, is caused by slippage, slippage, a condition where liquid flow rate becomes so low that excessive fallback begins to occur. Liquid falls back around the rising gas bubble. A smaller diameter tubing, giving higher velocities, should be used in this situation.
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VERTICAL FLOW CORRELATIONS There are various methods in place for determining the pressure losses that occur in flowing wells. It is not surprising that our prediction methods are not based on the exact solution of mathematical equations but rather on empirical or semi-empirical relationships. These relationships were developed by making certain assumptions about the applicable flow equations and then collecting data from a number of flowing wells under controlled conditions. The result is the publication of one or more correlations based on mathematical foundations and supported by observed field data. Early theoretical work in vertical flow analysis was undertaken by Versluys (1930). This was followed by the first practical application proposed by Poettmann and Carpenter (1952). Other important contributions include the work of Gilbert (1954), Duns and Ros (1963), Hagedorn and Brown (1965), Orkiszewski (1967), Govier and Aziz (1972), and Beggs and Brill (1973). We refer you to volume 1 of Brown’s text (1977) to learn how each of the theoretical and practical developments of these individuals evolved. Let us here summarize the approach and the important contributions of each. In reviewing these contributions we find it instructive to indicate the foundation of the work done, the pipe sizes to which the work applied, the fluids considered and, finally, to comment on the work of each. Versluys’ work was theoretically based and described vertical flow patterns. Poettman Poettm ann n and Car Carpen penter ter’s ’s work work was was semi semi-em -empir pirica icall and appl applied ied to to 2-, 2 - and and 3inch tubing. The fluids studied were oil, gas, and water. They developed practical solutions for GLR less than 1500 scf/bbl and for flow rates greater than 420 BOPD. In 1954, 1954, Gilbe Gilbert rt used used field field data data to inves investig tigate ate flow flow in 2-, 2-, 2 - and and 3-inc 3-inch h tubin tubing. g. He He investigated oil, gas, and water flowing wells and developed a practical set of pressure profile graphs that can easily be used in the field by the engineer. Duns and Ros combined experimental laboratory work with field studies for all pipe sizes and all fluids to develop one of the best correlations for all flow rates. Hagedorn and Brown undertook both field and experimental work. They considered each of the three phases of flowing fluids in 1- to 4-inch tubing and produced a very useful generalized correlation for all ranges of flow rate. Orkiszewski reviewed all of the methods that had been published to that date and then, from his observations, prepared a single composite correlation. This correlation applies to all pipe sizes and fluids, and it may be used to predict pressure losses for all ranges of flow. It is widely used as the basis for computer programs in industry today. In 1972, Govier and Aziz, in Canada, published their correlations which were based on laboratory and field data for all pipe sizes and all fluids. Their correlations were based on a mechanistic equation which had been tested against field data. In 1973, Beggs and Brill reported on the work being conducted at the University of Tulsa. They presented the resu results lts of of labora laborator tory y studie studies s on 1- and and 1 -inch -inch pipe pipe for for air air and and water. water. Thei Theirr correlation handles all ranges of multiphase flow for any pipe angle. The practical application of this work is the prediction of pressure losses in inclined or directionally drilled wells. Many more correlations have been published and work continues today in this important research area. 7
The above-mentioned theoretical and empirical studies have left us numerous vertical pressure loss prediction methods, presented originally as correlations or pressure traverse curves. Brown for example, in volume 2a of his text, presented a full set of pressure traverse curves. Many computer programs have been written using one or more of their correlations to predict pressure losses during flow. The question remains as to which of these methods is most accurate under a given set of conditions. Statistical comparisons (Lawson (Lawson and Brill, 1974) of several of the most widely used methods have been undertaken in order to determine their relative accuracy over a broad range of variables and to identify the strengths and weaknesses of each technique. No single pressure loss prediction method seems to be consistently superior under all ranges of production conditions. Comparisons of the methods of Poettmann and Carpenter, Duns and Ros, Hagedorn and Brown, Beggs and Brill, Govier and Aziz, and Orkiszewski show that the Hagedorn and Brown method has the best overall accuracy but that other methods perform better under different sets of variables and types of flow. Despite variations in accuracy among the methods tested, they are within the range of engineering accuracy for use in sizing well equipment and designing artificial lift installations. Estimates of flow rates and bottomhole flowing pressures may also be made with reasonable accuracy by using these pressure gradient curves. The ones published by Brown or Gilbert may certainly be used with confidence. Your company may have its own internally published set of curves which you may choose to use. Many companies have computer programs that calculate pressure losses in tubing using a combination of the various correlations. These are quite accurate because they are generally written so as to use each correlation over its range of greatest accuracy.
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THE USE OF PRESSURE TRAVERSE CURVES To better understand the basis for vertical flow calculations, and because they are quite accurate for engineering calculations, we should learn how pressure traverse or gradient curves are used. A typical set of pressure gradient or pressure or pressure traverse traverse curves are shown in Figure 1 .
Depth, on the vertical scale, runs downward from the surface to 10,000 ft. Pressure, on the horizontal scale, goes from 0 to about 2800 psi. As noted in the legend, the curves are generated using fixed values for the following parameters: • • • • • • •
tubing size producing rate, oil gravity gas gravity flowing fluid temperature water-oil ratio = zero (only oil is flowing) GLR = several selected values
If we have a well that matches these parameters, then the use of these curves is straightforward. To illustrate, assume that we have a well with the characteristics characteristics 9
shown in Figure 1, which is producing at a GLR of 200 SCF/Bbl. The length of the tubing string is 5000 ft. •
•
Case 1: Determine the tubing head pressure that corresponds to a known bottomhole
flowing pressure of 1600 psi: 1. First, First, we find find the point point at which which the "GLR=20 "GLR=200" 0" curve inter intersects sects a pressur pressure e of 1600 psi. 2. We note note that this this inters intersectio ection n correspon corresponds ds to a depth depth of about about 7200 7200 ft. 3. We continue continue to move move upward upward along along the "GLR=2 "GLR=200" 00" curve curve until until we have moved moved a vertical distance of 5000 ft, which is the length of the tubing string. This puts us at a point on the curve that corresponds to 2200 ft. 4. Finally, Finally, we trace trace a vertical vertical line upwards upwards from from this point, point, and and note that that the tubing tubing head pressure is 230 psi. Case 2: This is the more common case, where the surface THP is known (for this example, assume 400 psi) and we wish to estimate the bottomhole flowing pressure: 1. Starting Starting at the the top, at at a pressure pressure of 400 psi, psi, we trace trace a vertic vertical al line downw downward ard until we intersect the "GLR=200" curve. This takes us to a depth of 3450 ft. 2. We then move move down down along the the curve for for a vertical vertical distanc distance e of 5000 ft (i.e., (i.e., to 8450 ft). 3. We observe observe that the the flowing flowing bottomho bottomhole le pressure pressure at 8450 8450 ft is about about 2050 2050 psi.
Note that, in Case 1, if the well depth had been 10,000 ft instead of 5000 ft, we would have found in Step 3 that the pressure would have gone to zero before we had moved a total vertical distance of 10,000 ft (we would actually cross the zeropressure line at a depth of around 2400 ft). Under these circumstances we would be unable to calculate a positive tubing head pressure. This tells us that a 10,000-ft well could not flow at 1500 Bbl/D under the given conditions.
CALCULATING THE THP CURVE The shape of the THP for a given well can be varied by changing the magnitude of such variables as tubing size and sometimes gas-liquid ratios. From an engineering design point of view, we should change the variables over which we have control until we achieve optimal flow conditions. Example:: A corroded tubing string is being removed from a well and is to be Example replaced. In addition to 2
-inch tubing, we also have 1.9-inch and 3
-inch
tubing in inventory. What size tubing should be used to cause the well to flow at the maximum rate, given the following well data: THP = 170 psi depth = 5200 ft = 1850 psi GLR = 400 scf/bbl R
The present conditions with corroded tubing are: q = 250 BOPD
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Pwf = 1387 psi The reservoir pressure is above the bubble point. We begin by generating the IPR curve, in this case it is a straight line. Then, using pressure gradient curves, we calculate tubing head pressure curves for each size of tubing. The results are shown in Figure 1 .
At a tubin tubing g head head pressu pressure re of 170 psi, psi, the the 3
-inch -inch tubin tubing g will will allow allow a flow flow rate rate of
about about 425 425 BOPD, BOPD, the the 2 -inch -inch tubi tubing ng abou aboutt 525 525 BOPD, BOPD, and and the the 1.9-in 1.9-inch ch tubi tubing ng about 535 BOPD. The highest flow rate is provided by the smallest tubing. In practi practice, ce, the the 2 -inch -inch tubin tubing g would would proba probably bly be be chosen chosen for for its its streng strength th and and convenience of running tools, since its performance curve is nearly as good as that of 1.9-inch tubing. The design, then, is complete.
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HEADING One cause of wide variations in the tubing head pressure is called heading. heading. Heading refers to the periodic or cyclical surges in pressure and flow rate that occur in otherwise stable wells. Minor heading can occur at any time in the life of a well and under unpredictable conditions. Usually major events of heading occur late in the life of a well, when there are high GLRs. Heading is characterized at the surface by the production of intermittent slugs of liquid and gas at highly variable rates over a period of minutes. It normally occurs in the absence of a tubing-casing packer and is the result of gas bubbles bypassing the tubing and rising up the casing/tubing annulus. annulus. Unless the casing head pressure, (CHP), is bled off or equalized with the tubing head pressure, thereby decreasing production efficiency, the buildup of gas eventually lowers the level of fluid in the annulus to a point below thefoot of the tubing. Under these conditions, the gas blows around the tubing, and a slug of gas pushes the oil up the tubing at a rate higher than the well can sustain. This temporary surge lowers the flowing bottomhole pressure, increases the volume of the oil flowing into the well, and causes the fluid level in the annulus to rise again temporarily. The buildup of gas in the annulus starts the cycle over again. This is an inefficient use of the gas lifting potential. Heading can often signal the end of a well's flowing life, because the higher density/lower GOR oil being produced at a lower flow rate into the well immediately after the rate surge can cause a high enough drawdown to stop flow completely. Severe heading may cause unusual wear and tear on the well equipment and can interrupt flow prematurely. A few suggestions may be made to control heading. The first, of course, is to close off the annulus with a casing-tubing packer. This will eliminate annulus heading. A second option may be to bean back the well, thereby increasing the bottomhole pressure and with it the tendency to retain gas bubbles within the oil. We must be sure not to bean back the well so far as to kill it. A third possibility is to run a larger size tubing string so as to give lower vertical pressure losses and higher bottom-hole pressures. As with beaning, this will give lower GLRs but may lead to the killing of the well. Though its occurrence cannot be predicted with great accuracy, Duns and Ros (1963) have studied pressure losses during heading type flow conditions and have developed correlations that should be used for wells that are subject to heading.
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